Farb's conjecture on geometric rank-one manifolds

Let $M$ be a tame, complete, finite-volume $n$-manifold of bounded nonpositive curvature. A manifold has geometric rank one when it satisfies the rank-one condition used in the source. Farb's conjecture. If $M$ has geometric rank one, then there is a loop in $M$ that cannot be homotoped to leave every compact set.

This conjecture proposes that geometric rank one forces a loop to remain linked to the compact part of the manifold. The paper gives higher-dimensional counterexamples, so the conjecture is refuted.